1. Field of the Invention
The present invention relates to the optimization of development of underground reservoirs such as hydrocarbon reservoirs notably comprising a fracture network.
2. Description of the Prior Art
The petroleum industry, and more precisely reservoir exploration and development notably of petroleum reservoirs requires knowledge of the underground geology as perfectly as possible to efficiently provide evaluation of reserves, production modelling or development management. In fact, determining the location of a production well or of an injection well, the drilling mud composition, the completion characteristics, selection of a hydrocarbon recovery method (such as waterflooding for example) and of the parameters required for implementing the method (such as injection pressure, production flow rate, etc.) requires good knowledge of the reservoir. Reservoir knowledge notably is knowledge of the petrophysical properties of the subsoil at any point in space.
The petroleum industry has for a long time used field (in-situ) measurements with experimental modelling (performed in the laboratory) and/or numerical modelling (using softwares). Petroleum reservoir modelling thus is a technical stage that is essential for any reservoir exploration or development procedure. The goal of modelling is to provide a description of the reservoir.
Fractured reservoirs are an extreme type of heterogeneous reservoirs comprising two very different media, a matrix medium containing the major part of the oil in place and having a low permeability, and a fractured medium representing less than 1% of the oil in place and highly conductive. The fractured medium itself can be complex, with different sets of fractures characterized by their respective density, length, orientation, inclination and opening.
Engineers in charge of the development of fractured reservoirs need to perfectly know the role of fractures. What is referred to as fracture is a plane discontinuity of very small thickness in relation to the extent thereof, representing a rupture plane of a rock of the reservoir. On the one hand, knowledge of the distribution and of the behavior of these fractures allows optimizing the location and the spacing between wells to be drilled through the oil-bearing reservoir. On the other hand, the geometry of the fracture network conditions the fluid displacement, at the reservoir scale as well as the local scale where it determines elementary matrix blocks in which the oil is trapped. Knowing the distribution of the fractures is therefore also very helpful, at this stage, to the reservoir engineer who wants to calibrate the models he or she constructs to simulate the reservoirs in order to reproduce or to predict the past or future production curves. Geoscientists therefore have three-dimensional images of reservoirs allowing locating a large number of fractures.
Thus, in order to reproduce or to predict (i.e. “simulate”) the production of hydrocarbons when starting production of a reservoir according to a given production scenario (characterized by the position of the wells, the recovery method, etc.), reservoir engineers use a computing software referred to as reservoir simulator (or flow simulator) that calculates the flows and the evolution of the pressures within the reservoir, and the results of these computations enable them to predict and to optimize the reservoir in terms of flow rate and/or of amount of hydrocarbons recovered. Calculation of the reservoir behavior according to a given production scenario constitutes a “reservoir simulation”.
There is a well-known method for optimizing the development of a fluid reservoir traversed by a fracture network, wherein fluid flows through the reservoir are simulated through simplified but realistic modelling of the reservoir. This simplified representation, which is referred to as “double-medium approach”, is provided by Warren J. E. et al. in “The Behavior of Naturally Fractured Reservoirs”, SPE Journal (September 1963), 245-255. This technique considers the fractured medium as two continua exchanging fluids with one another: matrix blocks and fractures. One then refers to a “double medium” or “double porosity” model. Thus, “double-medium” modelling of a fractured reservoir discretizes this reservoir into two sets of superposed grid cells making up the “fracture” grid and the “matrix” grid. Each elementary volume of the fractured reservoir is thus conceptually represented by two grid cells, a “fracture” cell and a “matrix” cell, coupled to one another (i.e. exchanging fluids). In the reality of the fractured field, these two cells represent all of the matrix blocks delimited by fractures present at this point of the reservoir. In fact, in most cases, the cells have hectometric lateral dimensions (commonly 100 or 200 m) considering the size of the fields and the limited possibilities of simulation softwares in terms of computing capacity and time. The result thereof is that, for most fractured fields, the fractured reservoir elementary volume (cell) comprises innumerable fractures forming a complex network that delimits multiple matrix blocks of variable dimensions and shapes according to the geological context. Each constituent real block exchanges fluids with the surrounding fractures at a rate (flow rate) that is specific thereto because it depends on the dimensions and the shapes of this particular block.
In the face of such a geometrical complexity of the real medium, the approach is, for each reservoir elementary volume (grid cell), in representing the real fractured medium as a set of matrix blocks that are all identical, parallelepipedic, defined by an orthogonal and regular network of fractures oriented along the main directions of flow. A matrix block referred to as “representative” (of the real (geologic) distribution of the blocks), single and of parallelepipedic shape is thus defined for each cell. It is then possible to formulate and to calculate the matrix-fracture exchange flows for this “representative” block and to multiply the result by the number of such blocks in the elementary volume (cell) to obtain the flow at the scale of this cell.
In the “single permeability” version of the double-medium model, the flow of the fluids at the reservoir scale is assumed to occur only via the fractures (i.e. via the single fracture grid), fluid exchanges occurring locally between the fractures and the matrix blocks (that is between the two cells of a given pair of fracture and matrix cells representing the fractured porous reservoir at a given point of the field). In the “double permeability” version of this model, the fluid flow occurs within the two “fracture” and “matrix” media at the reservoir scale, still with local fracture-matrix fluid exchanges taking place locally between the fractures and the matrix blocks.
Such a representation (modelling) of the real (geological) fractured reservoir is used to reproduce, that is to “simulate”, the response (behavior) of the field as it is produced. Flow or transfer equations are therefore formulated, explicited and solved for each constituent cell of the model according to the method summed up hereafter. The set of mathematical equations applied to the double medium representing the fractured reservoir constitutes the double-medium reservoir simulator which is well known.
A reservoir simulator allows, from input data concerning on the one hand both media (matrix and fracture) and, on the other hand, the fluids that this double medium contains, to determine, at various times (time steps) and at each cell, the values of various parameters quantifying the state of these two media, such as saturations (oil, gas, water), pressures, concentrations, temperatures, etc. This simulator solves two sets of equations, one relative to the matrix medium, and the other relative to the fractured medium. As a matter of interest, it is noted that these equations express the mass (per constituent) and energy balances for each one of the “fracture” and “matrix” cells representing each elementary volumes of the real reservoir. These mass balances involve exchange flows between cells of the same medium (fracture or matrix) next to each other in space, the matrix-fracture exchange term that is the object of the present invention, a possible injection or production term if a well runs through the elementary volume considered, all of the aforementioned flow terms being equal to the matter or energy accumulation term of the cell being considered. Thus, the equations relative to the “matrix” medium and to the “fracture” medium at each point of the reservoir are coupled, via an exchange term describing the (matter or energy) exchange flows between the porous (matrix) rock and the fractures running therethrough. This matrix-fracture exchange modelling is essential because the matrix contains in most cases the main part of the reserves to be produced.
The method adopted to date for formulating these matrix-fracture exchanges is, for each pair of fracture and matrix cells discretizing the double-medium model: (on the one hand) determining the dimensions of identical matrix blocks (in dimension and shape) assumed to be representative of the complex real distribution of the blocks present in this elementary reservoir volume, and then formulating and calculating the matrix-fracture exchange flow according to the dimensions of the representative block thus calculated with this flow then being equal to the flow expressed for such a representative block multiplied by the number of such blocks in the cell considered.
Thus, the exchange formulations adopted to date in fractured reservoir simulators, based on a very simplified representation of this type of reservoir, prove to be very approximate and incapable of giving an accurate account of all of the exchange mechanisms likely to be involved, which include the pressure diffusivity, the capillarity, the gravity, the molecular diffusion, the conduction and viscous forces.
In fact, on the one hand, the exchange between matrix blocks and fractures is expressed at the (hectometric) scale of the cell of the simulation model, considering that a matrix block of fixed dimensions and shape is representative of (“equivalent to”) all of the real (geologic) blocks of the cell.
On the other hand, the exchange is assumed to be pseudo-permanent, that is the exchange flow at the boundaries of this equivalent block is proportional to the potential difference (for example: pressure difference, temperature difference, etc.) between the two matrix and fracture media. For each medium, this potential (temperature for example) is assumed to be uniform within a given medium, thus, in the present case, uniform (constant) within each block representative of the cell considered at the simulation time. Now, exchanges between fractures and blocks, notably if they involve several fluid phases, are not instantaneous. Furthermore, apart from the gravity and viscous entrainment effects (through fracture flow), these exchanges first concern the periphery of the blocks before they propagate to the center thereof. This spatial non-uniformity of the change of state of the matrix blocks also induces a non-stationary time evolution since the fluid of the fracture reaches much more rapidly the edges of the block than the center thereof. An accurate reproduction of the change of state of the blocks would thus require discretizing the block in order to simulate the displacements at a local scale (intra-block). The resultant of these flows at the block-fracture boundary then constitutes a much more accurate estimation of the matrix-fracture exchange over time.